Problem $10.$ Suppose the domain D is the universe. Using the following predicates: $$ C$($x$)$ : x is a child $$ B$($x$)$ : x is a book $$ L$($x$,$y$)$ : x likes y $$ E$($x$)$: x is educational Express the following sentences in predicate logic: $1.$ All children like books $2.$ Some child likes every single book $3.$ Not all children like all books $4.$ Some child does not like any book $5.$ There is a book that all children like $6.$ Books are always educational $7.$ Educational books are liked by children $8.$ Books are not always educational $9.$ No book, except for the educational ones, is liked by every child. $10.$ There is a child who likes all books that are not educational Solution $10.1.$ All children like books Vx$($c$($x$)+3$y$($B$($y$)$ AL$($x$,$y$)))$ V Jy $(((($x$)$ a Bly$))$ L$($x$,$ y$)1)$ QK$07$ A children like Textbook Mine books $4$x $($cca$)-$ y $($Bey$)$ L$($x$,$ y$))$ Yx$7$y $(($cens a Bly$))-$ Lix, y$))34$ Not like books all all children Text book Xxvy $($cens a Bly$)-$ Lix,y$))$ Mine TYN $($c$(*)-$ vy $($Bey$)$ Lix, y$))$